Ilya B. Simanovskii

Interfacial convection in multilayer systems

Introduction.- Types of convective instabilities in systems with an interface.- Benard problem in multilayer systems with undeformable interfaces.- Benard problem in multilayer systems with deformable interfaces.- Stability of flows.- Outlook.

Convective flows in a two-layer system with a temperature gradient along the interface

The nonlinear stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient, is investigated. Two types of boundary conditions, periodic boundary conditions and heat-insulated lateral walls, are considered. The nonlinear simulations of the wavy convective regimes for a particular set of fluids, are performed. The dependence of the direction of the wave propagation depends on two factors, which are studied, the ratio of the layers thicknesses and the Marangoni number.

Marangoni instability in ultrathin two-layer films

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film on a heated or cooled substrate, is considered. The problem is solved by means of a linear stability theory and nonlinear simulations. Nontrivial change of the droplet shape in the presence of the Marangoni effect, which manifests itself as the deformation of a “plateau” into an “inkpot,” is observed. The appearance of the threshold oscillations predicted by the linear stability theory is confirmed by nonlinear simulations.

Stability of thermocapillary flows with inclined temperature gradient

The stability of a two-layer return thermocapillary flow in the presence of an inclined temperature gradient is investigated. Both a linear stability analysis and nonlinear simulations have been performed for an air-water system

Decomposition of a two-layer thin liquid film flowing under the action of Marangoni stresses

The decomposition of a laterally heated two-layer film caused by intermolecular forces is considered. Long-wave nonlinear equations, which incorporate thermocapillary flows and the influence of the van der Waals forces, are derived. The main stages of the three-dimensional evolution of films are presented. The influence of the thermocapillary flow on the morphology and the evolution of unstable two-layer films is investigated. It is shown that the film instability leads typically to formation of droplets driven by the thermocapillary flow. Anisotropic coalescence of droplets and formation of rivulets are observed.

Thermocapillary convection in a multilayer system

The Marangoni–Benard instability for a symmetrical three‐layer system is examined theoretically. Linear stability analysis and nonlinear numerical simulations show that the ratio of the heat diffusivities determines the nature of the instability. Monotonic disturbances exist only when this parameter is far enough from one, the motion being driven by one interface. When the heat diffusivity ratio is close to one, oscillatory convection is observed. This is explained on a physical base: the oscillation rests on the coupling of both interfaces, which creates a flip–flop mechanism leading to a double inversion of the vortices rotation during one period of oscillation.

Influence of thermocapillary effect and interfacial heat release on convective oscillations in a two-layer system

The oscillatory convection for a real system of fluids under the joint action of buoyancy and thermocapillary effect or in the presence of the interfacial heat release is investigated. The nonlinear development of the oscillatory instability is studied. In the case of periodic boundary conditions, regimes of traveling waves and pulsating traveling waves are predicted. For different types of boundary conditions, the period doubling bifurcation is obtained. It is shown that the region of the Grashof number values, where nonlinear oscillations take place, is bounded both from below (by the mechanical equilibrium state) and from above (by the steady state).

Three-dimensional convection in a two-layer system with anomalous thermocapillary effect

At temperatures somewhat above room level, the interfacial tension between a 10 cS silicone oil and ethylene glycol increases with temperature, whereas it typically decreases for other systems of immiscible viscous fluids. The convective flows produced by the combined action of this so-called anomalous thermocapillary effect and buoyancy in this particular liquid–liquid system are studied by direct three-dimensional nonlinear simulation. The liquids are situated between rigid horizontal plates that are kept at different temperatures. A pseudospectral code is used to solve the evolution equations with periodic boundary conditions in the horizontal directions. Depending on the Grashof and Marangoni numbers G and M, the motionless state can either have a stationary or oscillatory instability. The corresponding finite amplitude solutions show a variety of regular structures (stationary rolls, stationary hexagons, pulsating hexagons, alternating rolls) as well as spatio-temporal chaos. The properties of the al...

Nonlinear Marangoni waves in a two-layer film in the presence of gravity

Longwave Marangoni convection in two-layer films under the action of gravity is considered. The analysis is carried out in the lubrication approximation. A linear stability analysis reveals the existence of monotonic and oscillatory instability modes, depending on the way of heating and the value of the Biot number. Numerical simulations are performed in the case of an oscillatory instability, which takes place by heating from above. Periodic boundary conditions are applied on the boundaries of the computational region. A sequence of nonlinear wavy regimes, which develop by the increase of the Galileo number, is studied. That sequence includes three-dimensional and two-dimensional structures. The multistability of wavy patterns with different spatial periods has been revealed.

Dynamics of ultra-thin two-layer films under the action of inclined temperature gradients

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film in the presence of an inclined temperature gradient is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. It has been found that for sufficiently large values of the ratio between the longitudinal and transverse Marangoni numbers, the real part of the linear growth rate does not depend on the direction of the wavenumber, except the case of nearly longitudinal disturbances. Numerous types of nonlinear evolution have been observed, among them are ordered systems of droplets, ‘splashes’, oblique waves, modulated transverse and longitudinal structures.